Unveiling the multilevel structure of midgap states in Sb-doped MoX2 (X=S, Se, Te

In this study, we use first-principles calculations to investigate the electronic and structural properties of $\text{Mo}{X}_{2}$ $(X=\text{S}, \mathrm{Se}, \mathrm{Te})$ monolayers doped with substitutional Sb atoms, with a central focus on the Sb(Mo) substitution. In ${\mathrm{MoS}}_{2}$, we observe that this substitution is energetically favored under S-rich conditions, where the ${\mathrm{S}}_{2}$ gaseous phase is likely to be present. This result is compatible with a recent experimental observation in Sb-doped ${\mathrm{MoS}}_{2}$ nanosheets grown by chemical vapor deposition. A similar behavior is found in ${\mathrm{MoSe}}_{2}$, but in ${\mathrm{MoTe}}_{2}$ the Sb(Mo) substitution is less likely to occur due to the possible absence of gaseous Te phases in experimental setups. In all cases, several impurity-induced states are found inside the band gap, with energies that span the entire gap. The Fermi energy is pinned a few tenths of eV above the top of the valence band, suggesting a predominant $p$-type behavior, and gap energies are slightly increased in comparison to the pristine systems. The orbital nature of these states is further investigated with projected and local density of states calculations, which reveal similarities to defect states induced by single Mo vacancies as well as their rehybridization with the $5s$ orbital from Sb. Additionally, we find that the band gap of the doped systems is increased in comparison with the pristine materials, in contrast with a previous calculation in Sb-doped ${\mathrm{MoS}}_{2}$ that predicts a gap reduction with a different assignment of valence band and impurity levels. We discuss the similarities, discrepancies, and the limitations of both calculations. We also speculate possible reasons for the experimentally observed redshifts of the $A$ and $B$ excitons in the presence of the Sb dopants in ${\mathrm{MoS}}_{2}$. We hope that these results spark future investigations on other aspects of the problem, particularly those concerning the effects of disorder and electron-hole interaction, and continue to reveal the potential of doped transition-metal dichalcogenides for applications in optoelectronic devices.